This invention relates to a method and apparatus for controlling a magnetic bearing with the intention of ensuring the stable operation of a rotor, suppressing the vibration caused by the imbalance of the rotor, and reducing the drive current.
FIG. 2 through FIG. 5 show various conventional control schemes for handling the vibration of a rotor supported by a magnetic bearing. The control scheme shown in FIG. 6 is not yet publicized at the time of filing of the application of the present invention.
Shown in FIG. 2 is the well-known servo feedback control system.
Shown in FIG. 3 is the automatic balancing system (ABS) described in Japanese patent publication JP-A-52-93852, and it may be called "N-cut system" as it derives from the operational property of eliminating the rotation-synchronous vibration component.
Shown in FIG. 4 is the critical damping control system described in Japanese patent publication JP-A-52-93853.
Shown in FIG. 5 is the N-cross system which is an improved version of the critical damping control system shown in FIG. 4, and it was proposed by the inventors of the present invention and described in Japanese patent publication JP-A-61-262225.
Before entering into the explanation of these prior art systems, the concept of magnetic bearing control against the rotor vibration will first be explained. A rotor supported by a magnetic bearing is subjected to the floating control in the x and y directions orthogonal to each other. Vibrations of the rotor in the x and y directions are detected as vibration signals x and y, respectively. From the vibration signal x, an input signal Px to a pair of power amplifiers 5X which drive electromagnets 2X for the x direction is produced.
The magnetic bearing produces a force, which acts on the rotor in the x direction, in proportion to the Px signal. Similarly, an input signal Py to power amplifiers 5Y for the y direction is produced from the vibration signal y. Control circuits (PID controllers) 4X and 4Y, produce Px from x and Py from y respectively, which provide indivisually for the x and y directions.
A tracking filter 7 receives a rotation signal which is a pulse signal generated at each revolution of the rotor and the vibration signals x and y, and extracts rotation-synchronous components x.sub.N and y.sub.N (will be termed simply "synchronous components", or generically called "N component") from the vibration signals x and y. A two-phase oscillator 10 is a device for producing, from the rotation signal, a cos(.OMEGA.t) signal and sin(.OMEGA.t) signal which are synchronous with the rotation.
A prime concern of the present invention is how to treat the rotation-synchronous components x.sub.N and Y.sub.N and the cos(.OMEGA.t) and sin(.OMEGA.t) signals.
Next, the prior art arrangements of FIG. 2 through FIG. 5 will be explained indivisually.
Prior art system of FIG. 2: A revolving body (rotor) 1 supported by the magnetic bearing can move off the central position (will be termed "neutral position") of the magnetic bearing due to the imbalance of the rotor or the influence of external forces, and therefore it is necessary to bring the rotor back to the neutral position through the control of the magnetic bearing. In the figure, two sets of electromagnets 2X and 2Y are disposed at the right, left upper and lower peripheries of the rotor 1, and the exciting currents supplied to these electromagnets are controlled thereby to control the rotor position in the magnetic bearing. Control circuits 4X and 4Y and power amplifiers 5X and 5Y are used to energize the electromagnets. The control circuits 4X and 4Y are PID controllers. The control circuit 4X receives the value x of displacement detected by a displacement sensor 3X for the x-axis direction, and the control circuit 4Y receives the value y of displacement detected by a displacement sensor 3Y for the y-axis direction. The displacement values x and y represent the displacements of the rotor position from the neutral position.
The control circuits 4X and 4Y produce control voltages P.sub.X and P.sub.Y from the displacement values, and supply them to the sets of power amplifiers 5X and 5Y. A pair of power amplifiers 5X supply exciting currents i.sub.x to the right and left electromagnets 2X of the magnetic bearing and another pair of power amplifiers 5Y supply exciting currents i.sub.y to upper and lower electromagnets 2Y so that the horizontal and vertical displacements of the rotor from the neutral position is corrected.
The control circuits 5X and 5Y base the operation on the processing of proportion (P), integration (I) and differentiation (D), and behave with various control characteristics depending on the manner of combination of the PID components.
The servo feedback control system of FIG. 2 is a fundamental control scheme for maintaining the rotor at the neutral position. However, it is not possible for the system to maintain the rotor at the neutral position over the entire range of rotor speed due to the presence of resonance points of bend mode in the high speed regions.
When the rotor speed is raised gradually, the resonance phenomena of the first and second orders of rigid mode appear. When the rotor speed is further raised gradually, the rotor becomes to exhibit the transition from a rigid body to a resilient moving body attributable to the imbalance of the rotor. The property of resilient body yields the resonance phenomena of the first and second orders of bend mode. The rotor speeds at which these resonance phenomena appear will be called "resonant frequencies" or "resonant points". The resonant points of the first and second orders of rigid mode and the resonant points of the first and second orders of bend mode may be called in series the resonant points of the first, second, third and fourth orders, respectively. The resonance curve has peak amplitudes Nc.sub.1, Nc.sub.2, Nc.sub.3 and Nc.sub.4 corresponding to these resonant points as shown in FIG. 7.
The servo feedback control system of FIG. 2 has its PID control parameters tuned so that the rotor is maintained at the neutral position in the whole range of speed including these resonant points. Actually, however, the control system of FIG. 2 can at most maintain the rotor at the neutral position against the vibration at the resonant points of the first and second orders of rigid mode. It is difficult for this servo feedback control system alone to cover the speed regions of the resonant points of the first and second orders of bend mode in maintaining the rotor at the neutral position.
Prior art system of FIG. 3: This system derived from the one shown in FIG. 2 is provided with a tracking filter 7, and the detected rotation signals x.sub.N and y.sub.N are fed back (negative feedback) to the inputs of the control circuits 4X and 4Y. The tracking filter 7 receives the displacement signals x and y and rotation pulses, and extracts the rotation-synchronous components x.sub.N and Y.sub.N. Further provided are subtracting nodes 9X and 9Y, on which the rotation-synchronous components x.sub.N and y.sub.N multiplied by a proportion factor .beta. (0 or 1), i.e., Bx.sub.N and By.sub.N, are subtracted from the displacement values x and y, and the results are delivered to the respective control circuits 4X and 4Y.
The circuit arrangement of FIG. 3, in which Bx.sub.N and By.sub.N are subtracted from x and y, causes the magnetic bearing to be unresponsive to the vibration attributable to the unbalanced rotation (insulation of vibration). Accordingly, the spring constant K.sub.N and damping constant C.sub.N are both zero for the rotation-synchronous components. The factor .beta. is set to 1 when the optional ABS control is to be applied, or otherwise it is set to 0. The ABS control has an advantage of eliminating the need of the exciting currents for the suppression of the imbalance-caused vibration. The ABS control is turned off (.beta.=0) during the passage of the resonant points, and it is turned on (.beta.=1) after the rotor speed has passed the resonant points.
Prior art system of FIG. 4: This system derived from the one shown in FIG. 2 is provided with a set of differentiation circuits 6X and 6Y and a tracking filter 7 with the intention of reducing the resonant amplitude of bend mode. The detected displacement values x and y delivered to the PID control circuits 4X and 4Y are also received by the differentiation circuits 6X and 6Y. The circuit 6X evaluates Kx+C(dx/dt) indicative of a value proportional to the chagne with time of the displacement x, and the rotation-synchronous tracking filter 7 detects a component, which is dependent on the rotor speed N, expressed as follows. EQU x.sub.0 =Kx.sub.N +C(dx.sub.N /dt) [Expression 1]
where K is the spring constant, and C is the damping constant.
Similarly, the differentiation circuit 6Y and rotation-synchronous tracking filter 7 detect a component, which is dependent on the rotor speed N, expressed as follows. EQU y.sub.0 =Ky.sub.N +C(dy.sub.N /dt) [Expression 2]
Based on the detection of the displacements and extraction of rotation-synchronous components x.sub.0 and y.sub.0, the magnetic bearing is controlled only against the vibration of rotation-synchronous imbalance. This system enables the adjustment of rigidity of the bearing (by varying the spring constant K) depending on the magnitude of displacement, and enables the adjustment of damping of the bearing displacement (by varying the damping constant C) depending on the rate of change with time. Consequently, the resonant amplitud of bend mode can be reduced. Generally, a differentiation circuit configured by electronic component parts creates high-frequency noises, and therefore its performance is limited to the approximation of mathematical operation at present.
Prior art system of FIG. 5: This system detects the rotor speed based on another scheme instead of using the differentiation circuits in the prior art system of FIG. 4. The system is intended for the case of the imbalance-caused confronting vibration, and it utilizes the fact that the differentiated value of vibration in the x-axis direction is proportional to the -y displacement value, and that in the y-axis direction is proportional to the x displacement value. Accordingly, the displacement values -y.sub.N and x.sub.N are used in place of the outputs of the differentiation circuits 6X and 6Y shown in FIG. 4. The rotation-synchronous components of the rate of change of both displacements can be extracted by the tracking filter 7.
The N-cross control can be accomplished perfectly by means of differentiation circuits, and it has an equivalent function of providing the damping constant C.sub.N against the imbalance-caused vibration. Accordingly, this is an optional system arrangement employed during the passage of the resonant point.
FIG. 6 discloses a relatively new system arrangement for achieving the suppression of vibration which was filed on May 20, 1992 as U.S. Ser. No. 07/885,980 by MATSUSHITA et al., titling "Balancing method for flexible rotor and a balancer applicable to the balancing method". In contrast to the foregoing prior art systems in FIGS. 1 to 5 which can fairly be categorized as feedback control systems because of the exciting current control by means of tracking filters in response to the displacement signals, the new system of FIG. 6 does not include a tracking filter which deals with the displacement signals x and y, and is categorized to be a feed forward (FF) control system, in which a counter vibrating force is generated in the opposite phase relation with the imbalance-caused vibration of each direction thereby to offset the vibration.
A two-phase oscillator 10 included in the system of FIG. 6 produces a sine wave signal Asin(.OMEGA.t+.phi.) and a cosine wave signal Acos(.OMEGA.t+.phi.) for the rotor speed .OMEGA. in synchronism with rotation pulses. The cosine wave signal Acos(.OMEGA.t+.phi.) multiplied by a proportional factor .gamma. is added to the output of the control circuit 4X and the sine wave signal Asin(.OMEGA.t+.phi.) multiplied by a proportional factor .gamma. is added to the output of the control circuit 4Y, and the resulting signals are used for the exciting current control of the magnetic bearing. By choosing the amplitude A and phase .phi. properly, counter vibration forces are generated to offset the imbalance-caused vibration forces at the resonant point, and consequently the resonant amplitude can be suppressed. This operation will be called "FF counter vibration".
The two-phase outputs may be applied at the inputs of the control circuits 4X and 4Y as shown by the dashed lines in FIG. 6. The FF control is another optional control function.
FIG. 8 is a table which summarizes the applied speed range and the property of control current (exciting current) carried out by the prior art systems in FIGS. 1 to 5 and above F.F. counter vibration.
The critical damping system described in Japanese patent publication JP-A-52-93853 produces the displacement rate signals dx/dt and dy/dt from the displacement signals x and y, and therefore it necessitates differentiation circuits, resulting in a complex circuit arrangement. This system involves another problem of a large vibration amplitude caused by the imbalance at the passage of the critical speed, which requires an increased amount of exciting current. The N-cross control described in Japanese patent publication JP-A-61-262225 involves the same problem of a large exciting current due to the introduction of the resonant vibration signals to the PID control circuit. These increased exciting currents demand a large dynamic range of power amplifiers, imposing the difficulty of practice. The ABS operation filters out the rotation-synchronous vibration components caused by the imbalance, and the exciting current can be reduced significantly. However, the activation of ABS control during the passage of the resonant creates an increased vibration, and therefore this control must be used only after the passage of the critical speed. Accordingly, the PID control without the accompaniment of ABS control during the passage of the critical speed expends a large amount of exciting current. The application of the ABS control further involves a problem of system instability such as drifting besides the insuffient reduction of imbalance-caused vibration.
FIG. 9 are examples of vibration characteristic curves showing the effectiveness of the ABS control. When attention is paid to the speed region near the third-order resonant point, the rotor is stable when the ABS control is absent or it is applied weakly. However, if the ABS control is strengthened, the vibration curve oscillates violently following the passage of the third-order resonant point. Accordingly, strong ABS control must be avoided in the speed regions near the resonant points, and it works effectively in a speed region distant from the resonant point, i.e., the speed region between the third-order and fourth-order resonant points in this example.
On this account, the ABS control based on the technical level at present is limited to the application in speed ranges which exclude the resonant regions.